Research article

Duplex PD inertial damping control paradigm for active power decoupling of grid-tied virtual synchronous generator


  • The growth of distributed generation significantly reduces the synchronous generators' overall rotational inertia, causing large frequency deviation and leading to an unstable grid. Adding virtual rotational inertia using virtual synchronous generators (VSG) is a promising technique to stabilize grid frequency. Due to coupled nature of frequency and active output power in a grid-tied virtual synchronous generator (GTVSG), the simultaneous design of transient response and steady state error becomes challenging. This paper presents a duplex PD inertial damping control (DPDIDC) technique to provide active power control decoupling in GTVSG. The power verses frequency characteristics of GTVSG is analyzed emphasizing the inconsistencies between the steady-state error and transient characteristics of active output power. The two PD controllers are placed in series with the generator's inertia forward channel and feedback channel. Finally, the performance superiority of the developed control scheme is validated using a simulation based study.

    Citation: Sue Wang, Jing Li, Saleem Riaz, Haider Zaman, Pengfei Hao, Yiwen Luo, Alsharef Mohammad, Ahmad Aziz Al-Ahmadi, NasimUllah. Duplex PD inertial damping control paradigm for active power decoupling of grid-tied virtual synchronous generator[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 12031-12057. doi: 10.3934/mbe.2022560

    Related Papers:

    [1] Xixia Ma, Rongsong Liu, Liming Cai . Stability of traveling wave solutions for a nonlocal Lotka-Volterra model. Mathematical Biosciences and Engineering, 2024, 21(1): 444-473. doi: 10.3934/mbe.2024020
    [2] S. Nakaoka, Y. Saito, Y. Takeuchi . Stability, delay, and chaotic behavior in a Lotka-Volterra predator-prey system. Mathematical Biosciences and Engineering, 2006, 3(1): 173-187. doi: 10.3934/mbe.2006.3.173
    [3] Pan Yang, Jianwen Feng, Xinchu Fu . Cluster collective behaviors via feedback pinning control induced by epidemic spread in a patchy population with dispersal. Mathematical Biosciences and Engineering, 2020, 17(5): 4718-4746. doi: 10.3934/mbe.2020259
    [4] Zigen Song, Jian Xu, Bin Zhen . Mixed-coexistence of periodic orbits and chaotic attractors in an inertial neural system with a nonmonotonic activation function. Mathematical Biosciences and Engineering, 2019, 16(6): 6406-6425. doi: 10.3934/mbe.2019320
    [5] Paul Georgescu, Hong Zhang, Daniel Maxin . The global stability of coexisting equilibria for three models of mutualism. Mathematical Biosciences and Engineering, 2016, 13(1): 101-118. doi: 10.3934/mbe.2016.13.101
    [6] Gayathri Vivekanandhan, Hamid Reza Abdolmohammadi, Hayder Natiq, Karthikeyan Rajagopal, Sajad Jafari, Hamidreza Namazi . Dynamic analysis of the discrete fractional-order Rulkov neuron map. Mathematical Biosciences and Engineering, 2023, 20(3): 4760-4781. doi: 10.3934/mbe.2023220
    [7] Biwen Li, Xuan Cheng . Synchronization analysis of coupled fractional-order neural networks with time-varying delays. Mathematical Biosciences and Engineering, 2023, 20(8): 14846-14865. doi: 10.3934/mbe.2023665
    [8] Yuanshi Wang, Donald L. DeAngelis . A mutualism-parasitism system modeling host and parasite with mutualism at low density. Mathematical Biosciences and Engineering, 2012, 9(2): 431-444. doi: 10.3934/mbe.2012.9.431
    [9] Xiaomeng Ma, Zhanbing Bai, Sujing Sun . Stability and bifurcation control for a fractional-order chemostat model with time delays and incommensurate orders. Mathematical Biosciences and Engineering, 2023, 20(1): 437-455. doi: 10.3934/mbe.2023020
    [10] Sai Zhang, Li Tang, Yan-Jun Liu . Formation deployment control of multi-agent systems modeled with PDE. Mathematical Biosciences and Engineering, 2022, 19(12): 13541-13559. doi: 10.3934/mbe.2022632
  • The growth of distributed generation significantly reduces the synchronous generators' overall rotational inertia, causing large frequency deviation and leading to an unstable grid. Adding virtual rotational inertia using virtual synchronous generators (VSG) is a promising technique to stabilize grid frequency. Due to coupled nature of frequency and active output power in a grid-tied virtual synchronous generator (GTVSG), the simultaneous design of transient response and steady state error becomes challenging. This paper presents a duplex PD inertial damping control (DPDIDC) technique to provide active power control decoupling in GTVSG. The power verses frequency characteristics of GTVSG is analyzed emphasizing the inconsistencies between the steady-state error and transient characteristics of active output power. The two PD controllers are placed in series with the generator's inertia forward channel and feedback channel. Finally, the performance superiority of the developed control scheme is validated using a simulation based study.



    The constituent members in a system mainly found in nature can be interacting with each other through cooperation and competition. Demonstrations for such systems involve biological species, countries, businesses, and many more. It's very much intriguing to investigate in a comprehensive manner numerous social as well as biological interactions existent in dissimilar species/entities utilizing mathematical modeling. The predation and the competition species are the most famous interactions among all such types of interactions. Importantly, Lotka [1] and Volterra [2] in the 1920s have announced individually the classic equations portraying population dynamics. Such illustrious equations are notably described as predator-prey (PP) equations or Lotka-Volterra (LV) equations. In this structure, PP/LV model represents the most influential model for interacting populations. The interplay between prey and predator together with additional factors has been a prominent topic in mathematical ecology for a long period. Arneodo et al. [3] have established in 1980 that a generalized Lotka-Volterra biological system (GLVBS) would depict chaos phenomena in an ecosystem for some explicitly selected system parameters and initial conditions. Additionally, Samardzija and Greller [4] demonstrated in 1988 that GLVBS would procure chaotic reign from the stabled state via rising fractal torus. LV model was initially developed as a biological concept, yet it is utilized in enormous diversified branches for research [5,6,7,8]. Synchronization essentially is a methodology of having different chaotic systems (non-identical or identical) following exactly a similar trajectory, i.e., the dynamical attributes of the slave system are locked finally into the master system. Specifically, synchronization and control have a wide spectrum for applications in engineering and science, namely, secure communication [9], encryption [10,11], ecological model [12], robotics [13], neural network [14], etc. Recently, numerous types of secure communication approaches have been explored [15,16,17,18] such as chaos modulation [18,19,20,21], chaos shift keying [22,23] and chaos masking [9,17,20,24]. In chaos communication schemes, the typical key idea for transmitting a message through chaotic/hyperchaotic models is that a message signal is nested in the transmitter system/model which originates a chaotic/ disturbed signal. Afterwards, this disturbed signal has been emitted to the receiver through a universal channel. The message signal would finally be recovered by the receiver. A chaotic model has been intrinsically employed both as receiver and transmitter. Consequently, this area of chaotic synchronization & control has sought remarkable considerations among differential research fields.

    Most prominently, synchronization theory has been in existence for over 30 years due to the phenomenal research of Pecora and Carroll [25] established in 1990 using drive-response/master-slave/leader-follower configuration. Consequently, many authors and researchers have started introducing and studying numerous control and synchronization methods [9,26,27,28,29,30,31,32,33,34,35,36] etc. to achieve stabilized chaotic systems for possessing stability. In [37], researchers discussed optimal synchronization issues in similar GLVBSs via optimal control methodology. In [38,39], the researchers studied the adaptive control method (ACM) to synchronize chaotic GLVBSs. Also, researchers [40] introduced a combination difference anti-synchronization scheme in similar chaotic GLVBSs via ACM. In addition, authors [41] investigated a combination synchronization scheme to control chaos existing in GLVBSs using active control strategy (ACS). Bai and Lonngren [42] first proposed ACS in 1997 for synchronizing and controlling chaos found in nonlinear dynamical systems. Furthermore, compound synchronization using ACS was first advocated by Sun et al. [43] in 2013. In [44], authors discussed compound difference anti-synchronization scheme in four chaotic systems out of which two chaotic systems are considered as GLVBSs using ACS and ACM along with applications in secure communications of chaos masking type in 2019. Some further research works [45,46] based on ACS have been reported in this direction. The considered chaotic GLVBS offers a generalization that allows higher-order biological terms. As a result, it may be of interest in cases where biological systems experience cataclysmic changes. Unfortunately, some species will be under competitive pressure in the coming years and decades. This work may be comprised as a step toward preserving as many currently living species as possible by using the proposed synchronization approach which is based on master-slave configuration and Lyapunov stability analysis.

    In consideration of the aforementioned discussions and observations, our primary focus here is to develop a systematic approach for investigating compound difference anti-synchronization (CDAS) approach in 4 similar chaotic GLVBSs via ACS. The considered ACS is a very efficient yet theoretically rigorous approach for controlling chaos found in GLVBSs. Additionally, in view of widely known Lyapunov stability analysis (LSA) [47], we discuss actively designed biological control law & convergence for synchronization errors to attain CDAS synchronized states.

    The major attributes for our proposed research in the present manuscript are:

    ● The proposed CDAS methodology considers four chaotic GLVBSs.

    ● It outlines a robust CDAS approach based active controller to achieve compound difference anti-synchronization in discussed GLVBSs & conducts oscillation in synchronization errors along with extremely fast convergence.

    ● The construction of the active control inputs has been executed in a much simplified fashion utilizing LSA & master-salve/ drive-response configuration.

    ● The proposed CDAS approach in four identical chaotic GLVBSs of integer order utilizing ACS has not yet been analyzed up to now. This depicts the novelty of our proposed research work.

    This manuscript is outlined as follows: Section 2 presents the problem formulation of the CDAS scheme. Section 3 designs comprehensively the CDAS scheme using ACS. Section 4 consists of a few structural characteristics of considered GLVBS on which CDAS is investigated. Furthermore, the proper active controllers having nonlinear terms are designed to achieve the proposed CDAS strategy. Moreover, in view of Lyapunov's stability analysis (LSA), we have examined comprehensively the biological controlling laws for achieving global asymptotical stability of the error dynamics for the discussed model. In Section 5, numerical simulations through MATLAB are performed for the illustration of the efficacy and superiority of the given scheme. Lastly, we also have presented some conclusions and the future prospects of the discussed research work in Section 6.

    We here formulate a methodology to examine compound difference anti-synchronization (CDAS) scheme viewing master-slave framework in four chaotic systems which would be utilized in the coming up sections.

    Let the scaling master system be

    ˙wm1= f1(wm1), (2.1)

    and the base second master systems be

    ˙wm2= f2(wm2), (2.2)
    ˙wm3= f3(wm3). (2.3)

    Corresponding to the aforementioned master systems, let the slave system be

    ˙ws4= f4(ws4)+U(wm1,wm2,wm3,ws4), (2.4)

    where wm1=(wm11,wm12,...,wm1n)TRn, wm2=(wm21,wm22,...,wm2n)TRn, wm3=(wm31,wm32,...,wm3n)TRn, ws4=(ws41,ws42,...,ws4n)TRn are the state variables of the respective chaotic systems (2.1)–(2.4), f1,f2,f3,f4:RnRn are four continuous vector functions, U=(U1,U2,...,Un)T:Rn×Rn×Rn×RnRn are appropriately constructed active controllers.

    Compound difference anti-synchronization error (CDAS) is defined as

    E=Sws4+Pwm1(Rwm3Qwm2),

    where P=diag(p1,p2,.....,pn),Q=diag(q1,q2,.....,qn),R=diag(r1,r2,.....,rn),S=diag(s1,s2,.....,sn) and S0.

    Definition: The master chaotic systems (2.1)–(2.3) are said to achieve CDAS with slave chaotic system (2.4) if

    limtE(t)=limtSws4(t)+Pwm1(t)(Rwm3(t)Qwm2(t))=0.

    We now present our proposed CDAS approach in three master systems (2.1)–(2.3) and one slave system (2.4). We next construct the controllers based on CDAS approach by

    Ui= ηisi(f4)iKiEisi, (3.1)

    where ηi=pi(f1)i(riwm3iqiwm2i)+piwm1i(ri(f3)iqi(f2)i), for i=1,2,...,n.

    Theorem: The systems (2.1)–(2.4) will attain the investigated CDAS approach globally and asymptotically if the active control functions are constructed in accordance with (3.1).

    Proof. Considering the error as

    Ei= siws4i+piwm1i(riwm3iqiwm2i),fori=1,2,3,.....,n.

    Error dynamical system takes the form

    ˙Ei= si˙ws4i+pi˙wm1i(riwm3iqiwm2i)+piwm1i(ri˙wm3iqi˙wm2i)= si((f4)i+Ui)+pi(f1)i(riwm3iqiwm2i)+piwm1i(ri(f3)iqi(f2)i)= si((f4)i+Ui)+ηi,

    where ηi=pi(f1)i(riwm3iqiwm2i)+piwm1i(ri(f3)iqi(f2)i), i=1,2,3,....,n. This implies that

    ˙Ei= si((f4)iηisi(f4)iKiEisi)+ηi= KiEi (3.2)

    The classic Lyapunov function V(E(t)) is described by

    V(E(t))= 12ETE= 12ΣE2i

    Differentiation of V(E(t)) gives

    ˙V(E(t))=ΣEi˙Ei

    Using Eq (3.2), one finds that

    ˙V(E(t))=ΣEi(KiEi)= ΣKiE2i). (3.3)

    An appropriate selection of (K1,K1,.......,Kn) makes ˙V(E(t)) of eq (3.3), a negative definite. Consequently, by LSA [47], we obtain

    limtEi(t)=0,(i=1,2,3).

    Hence, the master systems (2.1)–(2.3) and slave system (2.4) have attained desired CDAS strategy.

    We now describe GLVBS as the scaling master system:

    {˙wm11=wm11wm11wm12+b3w2m11b1w2m11wm13,˙wm12=wm12+wm11wm12,˙wm13=b2wm13+b1w2m11wm13, (4.1)

    where (wm11,wm12,wm13)TR3 is state vector of (4.1). Also, wm11 represents the prey population and wm12, wm13 denote the predator populations. For parameters b1=2.9851, b2=3, b3=2 and initial conditions (27.5,23.1,11.4), scaling master GLVBS displays chaotic/disturbed behaviour as depicted in Figure 1(a).

    Figure 1.  Phase graphs of chaotic GLVBS. (a) wm11wm12wm13 space, (b) wm21wm22wm23 space, (c) wm31wm32wm33 space, (d) ws41ws42ws43 space.

    The base master systems are the identical chaotic GLVBSs prescribed respectively as:

    {˙wm21=wm21wm21wm22+b3w2m21b1w2m21wm23,˙wm22=wm22+wm21wm22,˙wm23=b2wm23+b1w2m21wm23, (4.2)

    where (wm21,wm22,wm23)TR3 is state vector of (4.2). For parameter values b1=2.9851, b2=3, b3=2, this base master GLVBS shows chaotic/disturbed behaviour for initial conditions (1.2,1.2,1.2) as displayed in Figure 1(b).

    {˙wm31=wm31wm31wm32+b3w2m31b1w2m31wm33,˙wm32=wm32+wm31wm32,˙wm33=b2wm33+b1w2m31wm33, (4.3)

    where (wm31,wm32,wm33)TR3 is state vector of (4.3). For parameters b1=2.9851, b2=3, b3=2, this second base master GLVBS displays chaotic/disturbed behaviour for initial conditions (2.9,12.8,20.3) as shown in Figure 1(c).

    The slave system, represented by similar GLVBS, is presented by

    {˙ws41=ws41ws41ws42+b3w2s41b1w2s41ws43+U1,˙ws42=ws42+ws41ws42+U2,˙ws43=b2ws43+b1w2s41ws43+U3, (4.4)

    where (ws41,ws42,ws43)TR3 is state vector of (4.4). For parameter values, b1=2.9851, b2=3, b3=2 and initial conditions (5.1,7.4,20.8), the slave GLVBS exhibits chaotic/disturbed behaviour as mentioned in Figure 1(d).

    Moreover, the detailed theoretical study for (4.1)–(4.4) can be found in [4]. Further, U1, U2 and U3 are controllers to be determined.

    Next, the CDAS technique has been discussed for synchronizing the states of chaotic GLVBS. Also, LSA-based ACS is explored & the necessary stability criterion is established.

    Here, we assume P=diag(p1,p2,p3), Q=diag(q1,q2,q3), R=diag(r1,r2,r3), S=diag(s1,s2,s3). The scaling factors pi,qi,ri,si for i=1,2,3 are selected as required and can assume the same or different values.

    The error functions (E1,E2,E3) are defined as:

    {E1=s1ws41+p1wm11(r1wm31q1wm21),E2=s2ws42+p2wm12(r2wm32q2wm22),E3=s3ws43+p3wm13(r3wm33q3wm23). (4.5)

    The major objective of the given work is the designing of active control functions Ui,(i=1,2,3) ensuring that the error functions represented in (4.5) must satisfy

    limtEi(t)=0for(i=1,2,3).

    Therefore, subsequent error dynamics become

    {˙E1=s1˙ws41+p1˙wm11(r1wm31q1wm21)+p1wm11(r1˙wm31q1˙wm21),˙E2=s2˙ws42+p2˙wm12(r2wm32q2wm22)+p2wm12(r2˙wm32q2˙wm22),˙E3=s3˙ws43+p3˙wm13(r3wm33q3wm23)+p3wm13(r3˙wm33q3˙wm23). (4.6)

    Using (4.1), (4.2), (4.3), and (4.5) in (4.6), the error dynamics simplifies to

    {˙E1=s1(ws41ws41ws42+b3w2s41b1w2s41ws43+U1)+p1(wm11wm11wm12+b3w2m11b1w2m11wm13)(r1wm31q1wm21)+p1wm11(r1(wm31wm31wm32+b3w2m31b1w2m31wm33)q1(wm21wm21wm22+b3w2m21b1w2m21wm23),˙E2=s2(ws42+ws41ws42+U2)+p2(wm12+wm11wm12)(r2wm32q2wm22)+p2wm12(r2(wm32+wm31wm32)q2(wm22+wm21wm22)),˙E3=s3(b2ws43+b1w2s41ws43+U3)+p3(b2wm13+b1w2m11wm13)(r3wm33q3wm23)+p3wm13(r3(b2wm33+b1w2m31wm33)q3(b2wm23+b1w2m21wm23)). (4.7)

    Let us now choose the active controllers:

    U1= η1s1(f4)1K1E1s1, (4.8)

    where η1=p1(f1)1(r1wm31q1wm21)+p1wm11(r1(f3)1q1(f2)1), as described in (3.1).

    U2= η2s2(f4)2K2E2s2, (4.9)

    where η2=p2(f1)2(r2wm32q2wm22)+p2wm12(r2(f3)2q2(f2)2).

    U3= η3s3(f4)3K3E3s3, (4.10)

    where η3=p3(f1)3(r3wm33q3wm23)+p3wm13(r3(f3)3q3(f2)3) and K1>0,K2>0,K3>0 are gaining constants.

    By substituting the controllers (4.8), (4.9) and (4.10) in (4.7), we obtain

    {˙E1=K1E1,˙E2=K2E2,˙E3=K3E3. (4.11)

    Lyapunov function V(E(t)) is now described by

    V(E(t))= 12[E21+E22+E23]. (4.12)

    Obviously, the Lyapunov function V(E(t)) is +ve definite in R3. Therefore, the derivative of V(E(t)) as given in (4.12) can be formulated as:

    ˙V(E(t))= E1˙E1+E2˙E2+E3˙E3. (4.13)

    Using (4.11) in (4.13), one finds that

    ˙V(E(t))= K1E21K2E22K3E23<0,

    which displays that ˙V(E(t)) is -ve definite.

    In view of LSA [47], we, therefore, understand that CDAS error dynamics is globally as well as asymptotically stable, i.e., CDAS error E(t)0 asymptotically for t to each initial value E(0)R3.

    This section conducts a few simulation results for illustrating the efficacy of the investigated CDAS scheme in identical chaotic GLVBSs using ACS. We use 4th order Runge-Kutta algorithm for solving the considered ordinary differential equations. Initial conditions for three master systems (4.1)–(4.3) and slave system (4.4) are (27.5,23.1,11.4), (1.2,1.2,1.2), (2.9,12.8,20.3) and (14.5,3.4,10.1) respectively. We attain the CDAS technique among three masters (4.1)–(4.3) and corresponding one slave system (4.4) by taking pi=qi=ri=si=1, which implies that the slave system would be entirely anti-synchronized with the compound of three master models for i=1,2,3. In addition, the control gains (K1,K2,K3) are taken as 2. Also, Figure 2(a)(c) indicates the CDAS synchronized trajectories of three master (4.1)–(4.3) & one slave system (4.4) respectively. Moreover, synchronization error functions (E1,E2,E3)=(51.85,275.36,238.54) approach 0 as t tends to infinity which is exhibited via Figure 2(d). Hence, the proposed CDAS strategy in three masters and one slave models/systems has been demonstrated computationally.

    Figure 2.  CDAS synchronized trajectories of GLVBS between (a) ws41(t) and wm11(t)(wm31(t)wm21(t)), (b) ws42(t) and wm12(t)(wm32(t)wm22(t)), (c) ws43(t) and wm13(t)(wm23(t)wm13(t)), (d) CDAS synchronized errors.

    In this work, the investigated CDAS approach in similar four chaotic GLVBSs using ACS has been analyzed. Lyapunov's stability analysis has been used to construct proper active nonlinear controllers. The considered error system, on the evolution of time, converges to zero globally & asymptotically via our appropriately designed simple active controllers. Additionally, numerical simulations via MATLAB suggest that the newly described nonlinear control functions are immensely efficient in synchronizing the chaotic regime found in GLVBSs to fitting set points which exhibit the efficacy and supremacy of our proposed CDAS strategy. Exceptionally, both analytic theory and computational results are in complete agreement. Our proposed approach is simple yet analytically precise. The control and synchronization among the complex GLVBSs with the complex dynamical network would be an open research problem. Also, in this direction, we may extend the considered CDAS technique on chaotic systems that interfered with model uncertainties as well as external disturbances.

    The authors gratefully acknowledge Qassim University, represented by the Deanship of Scientific Research, on the financial support for this research under the number 10163-qec-2020-1-3-I during the academic year 1441 AH/2020 AD.

    The authors declare there is no conflict of interest.



    [1] C. Hepburn, Y. Qi, N. Stern, B. Ward, X. Chun, D. Zenghelis, Towards carbon neutrality and China's 14th Five-Year Plan: clean energy transition, sustainable urban development, and investment priorities, Environ. Sci. Ecotechnol., 8 (2021), 100–130. https://doi.org/10.1016/J.ESE.2021.100130 doi: 10.1016/J.ESE.2021.100130
    [2] Q. C. Zhong, T. Holnick, Control of Power Inverters in Renewable Energy and Smart Grid Integration, John Wiley & Sons, 2012. https://doi.org/10.1002/9781118481806
    [3] L. Z. Yao, B. Yang, H. F. Cui, J. Zhuang, J. Ye, J. Xue, Challenges and progresses of energy storage technology and its application in power systems, J. Mod. Power Syst. Clean Energy, 4 (2016), 519–528. https://doi.org/10.1007/s40565-016-0248-x doi: 10.1007/s40565-016-0248-x
    [4] Y. W. Wang, B. Y. Liu, S. X. Duan, Transient performance comparison of modified VSG controlled grid-tied converter, in 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), IEEE, (2019), 3300–3303. https://doi.org/10.1109/APEC.2019.8722121
    [5] M. Q. Mao, C. Qian, Y. Ding, Decentralized coordination power control for islanding microgrid based on PV/BES-VSG, CPSS Trans. Power Electron. Appl., 3 (2018), 14–24. https://doi.org/10.24295/CPSSTPEA.2018.00002 doi: 10.24295/CPSSTPEA.2018.00002
    [6] W. H. Wu, Y. D. Chen, L. M. Zhou, A. Luo, X. Zhou, Z. He, et al., Sequence impedance modeling and stability comparative analysis of voltage-controlled VSGs and current-controlled VSGs, IEEE Trans. Ind. Electron., 66 (2018), 6460–6472. https://doi.org/10.1109/TIE.2018.2873523 doi: 10.1109/TIE.2018.2873523
    [7] K. Shi, H. H. Ye, W. T. Song, G. L. Zhou, Virtual inertia control strategy in microgrid based on virtual synchronous generator technology, IEEE Access, 6 (2018), 27949–27957. https://doi.org/10.1109/access.2018.2839737 doi: 10.1109/access.2018.2839737
    [8] H. S. Hlaing, J. Liu, Y. Miura, H. Bevrani, T. Ise, Enhanced performance of a stand-alone gas-engine generator using virtual synchronous generator and energy storage system, IEEE Access, 7 (2019), 176960–176970. https://doi.org/10.1109/ACCESS.2019.2957890 doi: 10.1109/ACCESS.2019.2957890
    [9] S. Saadatmand, M. Nia, P. Shamsi, M. Ferdowsi, D. C. Wunsch, Neural network predictive controller for grid-connected virtual synchronous generator, in 2019 North American Power Symposium (NAPS), IEEE, (2019), 1–6. https://doi.org/10.1109/NAPS46351.2019.900038
    [10] L. M. A Torres, L. A. C Lopes, T. L. A. Miguel, C. J. R. Espinoza, Self-tuning virtual synchronous machine: A control strategy for energy storage systems to support dynamic frequency control, IEEE Trans. Energy Convers., 29 (2014), 833–840. https://doi.org/10.1109/TEC.2014.2362577 doi: 10.1109/TEC.2014.2362577
    [11] M. Guan, W. Pan, J. Zhang, Q. Hao, J. Cheng, X. Zheng, Synchronous generator emulation control strategy for voltage source converter (VSC) stations, IEEE Trans. Power Syst., 30 (2015), 3093–3101. https://doi.org/10.1109/TPWRS.2014.2384498 doi: 10.1109/TPWRS.2014.2384498
    [12] H. Wu, X. B. Ruan, D. Yang, X. Chen, W. Zhao, Z. Lv, et al., Small-signal modeling and parameters design for virtual synchronous generators, IEEE Trans. Ind. Electron., 63 (2016), 4292–4303. https://doi.org/10.1109/TIE.2016.2543181 doi: 10.1109/TIE.2016.2543181
    [13] H. Xu, X. Zhang, F. Liu, Virtual synchronous generator control strategy based on lead-lag link virtual inertia, Proc. CSEE, 37 (2017), 1918–1926. https://doi.org/10.13334/j.0258-8013.pcsee.160205 doi: 10.13334/j.0258-8013.pcsee.160205
    [14] J. Liu, Y. Miura, T. Ise, Comparison of dynamic characteristics between virtual synchronous generator and droop control in inverter-based distributed generators, IEEE Trans. Power Electron., 31 (2015), 3600–3611. https://doi.org/10.1109/TPEL.2015.2465852 doi: 10.1109/TPEL.2015.2465852
    [15] K. Shi, H. Ye, P. Xu, D. Zhao, L. Jiao, Low-voltage ride through control strategy of virtual synchronous generator based on the analysis of excitation state, IET Gener. Transm. Distrib., 12 (2018), 2165–2172. https://doi.org/10.1049/iet-gtd.2017.1988 doi: 10.1049/iet-gtd.2017.1988
    [16] J. Li, B. Wen, H. Wang, Adaptive virtual inertia control strategy of VSG for micro-grid based on improved bang-bang control strategy, IEEE Access, 7 (2019), 39509–39514. https://doi.org/10.1109/ACCESS.2019.2904943 doi: 10.1109/ACCESS.2019.2904943
    [17] J. W. Ding, J. B. Zhang, Z. H. Ma, VSG inertia and damping coefficient adaptive control, in 2020 Asia Energy and Electrical Engineering Symposium (AEEES), IEEE, (2020), 431–435. https://doi.org/10.1109/AEEES48850.2020.9121526
    [18] J. Alipoor, Y. Miura, T. Ise, Power system stabilization using virtual synchronous generator with alternating moment of inertia, IEEE J. Emerging Sel. Top. Power Electron., 3 (2015), 451–458. https://doi.org/10.1109/JESTPE.2014.2362530 doi: 10.1109/JESTPE.2014.2362530
    [19] H. Z. Xu, X. Zhang, F. Liu, Control strategy of virtual synchronous generator based on differential compensation virtual inertia, Autom. Electr. Power Syst., 41 (2017), 96–102. https://doi.org/10.7500/AEPS20160420001 doi: 10.7500/AEPS20160420001
    [20] M. X. Li, Y. Wang, N. Y. Xu, Virtual synchronous generator control strategy based on bandpass damping power feedback, Trans. China Electrotech. Soc., 33 (2018), 2176–2185. https://doi.org/10.19595/j.cnki.1000-6753.tces.170201 doi: 10.19595/j.cnki.1000-6753.tces.170201
    [21] X. Li, G. Chen, M. Ali, Improved virtual synchronous generator with transient damping link and its seamless transfer control for cascaded H-bridge multilevel converter-based energy storage system, IET Electr. Power Appl., 13 (2019), 1535–1543. https://doi.org/10.1049/iet-epa.2018.5722 doi: 10.1049/iet-epa.2018.5722
    [22] C. Li, Y. Q. Yang, N. Mijatovic, T. Dragicevic, Frequency stability assessment of grid-forming VSG in framework of MPME with feedforward decoupling control strategy, IEEE Trans. Ind. Electron., 69 (2022), 6903–6913. https://doi.org/10.1109/TIE.2021.3099236 doi: 10.1109/TIE.2021.3099236
    [23] H. Xu, C. Yu, C. Liu, Q Wang, X. Zhang, An improved virtual inertia algorithm of virtual synchronous generator, J. Mod. Power Syst. Clean Energy, 8 (2019), 377–386. https://doi.org/10.35833/MPCE.2018.000472 doi: 10.35833/MPCE.2018.000472
    [24] Z. Lv, W. Sheng, H. Liu, L. Sun, M. Wu, Application and challenge of virtual synchronous machine technology in power system, in Proceedings of the CSEE, 37 (2017), 349–359. https://doi.org/10.13334/j.0258-8013.pcsee.161604
    [25] K. Shi, G. Zhou, P. Xu, H. Ye, F. Tan, The integrated switching control strategy for grid-connected and islanding operation of micro-grid inverters based on a virtual synchronous generator, Energies, 11 (2018), 1–20. https://doi.org/10.3390/en11061544 doi: 10.3390/en11061544
    [26] J. He, Y. W. Li, J. M Guerrero, F. Blaabjerg, J. C. Vasquez, An islanding microgrid power sharing approach using enhanced virtual impedance control scheme, IEEE Trans. Power Electron., 28 (2013), 5272–5282. https://doi.org/10.1109/TPEL.2013.2243757 doi: 10.1109/TPEL.2013.2243757
    [27] D. Chen, Y. Xu, A. Q. Huang, Integration of DC microgrids as virtual synchronous machines into the AC grid, IEEE Trans. Ind. Electron., 64 (2017), 7455–7466. https://doi.org/10.1109/TIE.2017.2674621 doi: 10.1109/TIE.2017.2674621
    [28] Y. C. Zhu, M. F. Peng, X. Yu, Research on improved virtual synchronous generator based on differential compensation link, in 2018 IEEE 3rd International Conference on Integrated Circuits and Microsystems (ICICM), (2018), 259–263. https://doi.org/10.1109/ICAM.2018.8596677
  • This article has been cited by:

    1. Cheng-Jun 成俊 Xie 解, Xiang-Qing 向清 Lu 卢, Finite time hybrid synchronization of heterogeneous duplex complex networks via time-varying intermittent control, 2025, 34, 1674-1056, 040601, 10.1088/1674-1056/adacc6
    2. Cheng-jun Xie, Ying Zhang, Qiang Wei, Finite time internal and external synchronisation control for multi-layer complex networks with multiple time-varying delays via rapid response intermittent control, 2025, 0020-7179, 1, 10.1080/00207179.2025.2503307
  • Reader Comments
  • © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2558) PDF downloads(117) Cited by(3)

Figures and Tables

Figures(22)  /  Tables(3)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog